| A Different Version of Flett＇s Mean Value Theorem and an Associated Functional Equation |
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| 作者姓名： | ThomasRIEDEL MaciejSABLIK |
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| 作者单位： | [1]DepartmentofMathematics,UniversityofLouisville,Louisville,KY40292,USA [2]InstituteofMathematics,SilesianUniversity,Bankowa14,40007Katowice,Poland |
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| 摘 要： | In this paper we present a mean value theorem derived from Flett‘s mean value theorem. It turns out that cubic polynomials have the midpoint of the interval as their mean value point. To answer what class of functions have this property, we consider a functional equation associated with this mean value theorem. This equation is then solved in a general setting on abelian groups.
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| 关 键 词： | Flett均值定理 功能方程 多项式 实值函数 |
| 收稿时间： | 27 November 2002 |
A Different Version of Flett's Mean Value Theorem
and an Associated Functional Equation |
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| ThomasRIEDEL MaciejSABLIK.A Different Version of Flett's Mean Value Theorem
and an Associated Functional Equation[J].Acta Mathematica Sinica,2004,20(6):1073-1078. |
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| Authors: | Email author" target="_blank">Thomas?RiedelEmail author Maciej?Sablik |
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| Institution: | (1) Department of Mathematics, University of Louisville, Louisville, KY 40292, USA;(2) Institute of Mathematics, Silesian University, Bankowa 14, 40007 Katowice, Poland |
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| Abstract: | In this paper we present a mean value theorem derived from Flett's mean value theorem.
It turns out that cubic polynomials have the midpoint of the interval as their mean value point. To
answer what class of functions have this property, we consider a functional equation associated with
this mean value theorem. |
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| Keywords: | Flett's mean value theorem Functional equations Polynomial functions |
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